Answer:
0.014 or 1.4% of connectors fail during the warranty period.
Step-by-step explanation:
Consider the provided information.
Let: D = electrical connector is dry
D' = electrical connector is not kept dry (i.e., is wet)
F = connector fails during warranty period
F' = connector does not fail during warranty period
90% of the connectors are kept dry
That means P(D)=0.9
10% are wet,
P(D')=0.1
The probability is 1% that an electrical connector that is kept dry fails during the warranty period, i.e.
P(F|D)=0.01
If the connector is ever wet, the probability of a failure during the warranty period is 5%, i.e.
P(F|D')=0.05
[tex]P(F)=P(D)\times P(F|D)+P(D')\times P(F|D')\\P(F)=0.9\times 0.01+0.1\times 0.05\\P(F)=0.014[/tex]
Hence, 0.014 or 1.4% of connectors fail during the warranty period.
